Question

Solve the inequality. Graph and check your solution.

$\mathbf{5}\mathbf{y}\mathbf{+}\mathbf{2}\le \mathbf{y}\mathbf{+}\mathbf{34}$

Short answer

Solution of the inequality is$y\le 8$ .

Step-by-step solution

Step-1- Solve the inequality

$5y+2\le y+34$

Subtract 2 and y from both the sides.

$\begin{array}{c}5y+2\le y+34\\ 5y+2-2-y\le y+34-2-y\end{array}$

Divide both sides by 4.

$\begin{array}{c}y\le \frac{32}{4}\\ y\le 8\end{array}$

Step-2- Graph the inequality

The solution of the inequality is$y\le 8$ .

That means, all values $y\le 8$satisfy the inequality. So, the graph can be given as shown below.

Step-3- Check the solution

To check the solution, take any random number,$y\le 8$and substitute in the original inequality and observe the result.

Take$y=0$.

Then,

$\begin{array}{c}5\times 0+2\le 0+34\\ 0+2\le 34\\ 2\le 34\end{array}$

The result$2\le 34$ is true. So, the solution $y\le 8$is correct.